A 0.5-m high toddler is playing 10 m in front of a convex mirror with radius of curvature of 7 m. What is the location of his image? What is the height of his image?

Answer 1

Use the mirror equation 1/d_o + 1/d_i = 1/f, but the focal length is negative for convex mirrors. 1/d_i = -1/7 - 1/10 yields an image distance of d_i = -4.₁₂ m (I'm putting non-significant figures as subscripts). The negative sign (and a convex mirror in general) puts the image behind the mirror.

Magnification m = -d_i /d_o = +4.₁₂ / 10 = 0.4₁₂, so height = 0.5•m = 0.2₁ m.